• Author: Dace Apšvalka
  • Date: August 2024
  • conda environment: I used the fMRI workshop's conda environment to run this notebook and any accompanied scripts.

fMRI Data Analysis: Group-Level Analysis¶

Once you have beta (or contrast) maps for conditions (or contrasts) from all subjects, you can perform group-level statistics. Importantly, all subject first-level results need to be in common space, e.g., MNI, to perform voxel-wise group analyses. Group-level analysis allows you to make inferences about the population, rather than individual subjects, by assessing common patterns across participants. Common statistical methods for group-level analysis include one-sample or paired t-tests, as well as more complex mixed-effects models, depending on your study design.

In this tutorial, we are adopting a mixed-effects model approach. We will incorporate the beta maps of all nine conditions into a single design matrix with subject-specific regressors. This approach can capture more of the explained variance by accounting for both condition effects and subject-level variability in one model. This differs from a one-sample t-test on first-level contrast estimates, where the model only assesses the variance in the contrast across subjects. The one-sample t-test simplifies the analysis but doesn't explicitly model within-subject variability or interactions across conditions, which can lead to a less comprehensive understanding of the underlying effects. The mixed-effects model approach handles both within- and between-subject variability, allowing for a more nuanced analysis of comparisons and potentially reducing unexplained variance.

Mixed-effects models are often analysed with ANOVA, which Nilean's second_level_model.compute_contrast would do. However, there isn’t a straightforward way with Nilearn to check and account for non-sphericity in the data (see Rik’s Stats tutorial on ANOVA for the importance of this). To mitigate this issue, we can use Nilearn's non-parametric inference, which we will employ for our final results in this group-level analysis example.

Here is a recommended viewing to help better understand the principles of the group-level analysis:

In [1]:
from IPython.display import YouTubeVideo
YouTubeVideo('__cOYPifDWk', width=560, height=315)
Out[1]:

Table of contents

  1. Import required packages and set up some stuff
  2. Retrieve First-Level results
  3. Displaying subject Effects-Of-Interest z-maps
  4. Specify the second-level model
    4.1. Design matrix
    4.2. Contrasts
    4.3. Model specification and fit
  5. Computing contrasts and plotting result maps
    5.1. False-positive-rate with cluster-forming threshold
    5.2. FWE correction using Bonferroni correction
    5.3. FWE correction using non-parametric permutation testing
  6. Summary results
    6.1. Using atlasreader package
    6.2. Nilearn's report

1. Import required packages and set up some stuff¶

In [2]:
# The conda environment used for this tutorial is available here: https://github.com/MRC-CBU/COGNESTIC/blob/main/mri_environment.yml 

import os.path as op # for file path operations
import glob # to search for files using regex

import pandas as pd # for data manipulation
import numpy as np # for numerical operations

from bids.layout import BIDSLayout # to fetch data from BIDS-compliant datasets

import matplotlib.pyplot as plt # for basic plotting

import nibabel as nib # NiBabel, to read and write neuroimaging data, https://nipy.org/nibabel/

# Nilearn modules, for the analysis of brain volumes, plotting, etc., https://nilearn.github.io/
from nilearn.plotting import plot_glass_brain, plot_design_matrix, plot_contrast_matrix, plot_stat_map, view_img, view_img_on_surf
from nilearn.glm.second_level import SecondLevelModel
from nilearn.glm.thresholding import threshold_stats_img
from nilearn.datasets import load_mni152_template
from nilearn.glm.second_level import non_parametric_inference

from atlasreader import create_output # For generating result tables https://github.com/miykael/atlasreader

The Python package you are importing, AtlasReader, is licensed under the
BSD-3 license; however, the atlases it uses are separately licensed under more
restrictive frameworks.
By using AtlasReader, you agree to abide by the license terms of the
individual atlases. Information on these terms can be found online at:
https://github.com/miykael/atlasreader/tree/master/atlasreader/data
In [3]:
# MNI152 template will be used as a backgound for plotting MNI-space ROIs
mni152_template = load_mni152_template()

2. Retrieve First-Level results¶

For the group analysis, we will use the single-condition contrast estimate (beta estimate) maps for all nine conditions. Because we saved the results in BIDS format, we can us PyBIDS to retrieve the subject-level results.

In [4]:
# --- Set up the paths to the data and results folders
fmri_data_dir = 'FaceProcessing/data' # data in BIDS format
fmri_results_dir = 'FaceProcessing/results' # results in BIDS format

# --- Set up the BIDS layout
layout = BIDSLayout(fmri_data_dir, derivatives = True)

# Attach the results folder to the layout. It must complay with BIDS standards. 
# And must include dataset_description.json file!
layout.add_derivatives(op.join(fmri_results_dir, "first-level"))

Specify which conditions to include in the analysis and retrieve their effect files from the first-level results.

In [5]:
conditions = ['FAMOUS1', 'FAMOUS2dl', 'FAMOUS2im', 'UNFAMILIAR1', 'UNFAMILIAR2dl', 'UNFAMILIAR2im', 'SCRAMBLED1', 'SCRAMBLED2dl', 'SCRAMBLED2im']

effect_files = layout.get(desc=conditions, suffix='effect', extension='.nii.gz', return_type='filename')

# print to see if it found what we expexted
print(f"Found {len(effect_files)} effect files:")
print(*effect_files, sep="\n")

Found 144 effect files:
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-01/sub-01_task-faceprocessing_desc-FAMOUS1_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-01/sub-01_task-faceprocessing_desc-FAMOUS2dl_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-01/sub-01_task-faceprocessing_desc-FAMOUS2im_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-01/sub-01_task-faceprocessing_desc-SCRAMBLED1_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-01/sub-01_task-faceprocessing_desc-SCRAMBLED2dl_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-01/sub-01_task-faceprocessing_desc-SCRAMBLED2im_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-01/sub-01_task-faceprocessing_desc-UNFAMILIAR1_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-01/sub-01_task-faceprocessing_desc-UNFAMILIAR2dl_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-01/sub-01_task-faceprocessing_desc-UNFAMILIAR2im_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-02/sub-02_task-faceprocessing_desc-FAMOUS1_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-02/sub-02_task-faceprocessing_desc-FAMOUS2dl_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-02/sub-02_task-faceprocessing_desc-FAMOUS2im_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-02/sub-02_task-faceprocessing_desc-SCRAMBLED1_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-02/sub-02_task-faceprocessing_desc-SCRAMBLED2dl_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-02/sub-02_task-faceprocessing_desc-SCRAMBLED2im_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-02/sub-02_task-faceprocessing_desc-UNFAMILIAR1_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-02/sub-02_task-faceprocessing_desc-UNFAMILIAR2dl_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-02/sub-02_task-faceprocessing_desc-UNFAMILIAR2im_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-03/sub-03_task-faceprocessing_desc-FAMOUS1_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-03/sub-03_task-faceprocessing_desc-FAMOUS2dl_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-03/sub-03_task-faceprocessing_desc-FAMOUS2im_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-03/sub-03_task-faceprocessing_desc-SCRAMBLED1_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-03/sub-03_task-faceprocessing_desc-SCRAMBLED2dl_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-03/sub-03_task-faceprocessing_desc-SCRAMBLED2im_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-03/sub-03_task-faceprocessing_desc-UNFAMILIAR1_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-03/sub-03_task-faceprocessing_desc-UNFAMILIAR2dl_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-03/sub-03_task-faceprocessing_desc-UNFAMILIAR2im_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-04/sub-04_task-faceprocessing_desc-FAMOUS1_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-04/sub-04_task-faceprocessing_desc-FAMOUS2dl_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-04/sub-04_task-faceprocessing_desc-FAMOUS2im_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-04/sub-04_task-faceprocessing_desc-SCRAMBLED1_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-04/sub-04_task-faceprocessing_desc-SCRAMBLED2dl_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-04/sub-04_task-faceprocessing_desc-SCRAMBLED2im_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-04/sub-04_task-faceprocessing_desc-UNFAMILIAR1_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-04/sub-04_task-faceprocessing_desc-UNFAMILIAR2dl_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-04/sub-04_task-faceprocessing_desc-UNFAMILIAR2im_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-05/sub-05_task-faceprocessing_desc-FAMOUS1_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-05/sub-05_task-faceprocessing_desc-FAMOUS2dl_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-05/sub-05_task-faceprocessing_desc-FAMOUS2im_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-05/sub-05_task-faceprocessing_desc-SCRAMBLED1_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-05/sub-05_task-faceprocessing_desc-SCRAMBLED2dl_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-05/sub-05_task-faceprocessing_desc-SCRAMBLED2im_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-05/sub-05_task-faceprocessing_desc-UNFAMILIAR1_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-05/sub-05_task-faceprocessing_desc-UNFAMILIAR2dl_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-05/sub-05_task-faceprocessing_desc-UNFAMILIAR2im_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-06/sub-06_task-faceprocessing_desc-FAMOUS1_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-06/sub-06_task-faceprocessing_desc-FAMOUS2dl_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-06/sub-06_task-faceprocessing_desc-FAMOUS2im_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-06/sub-06_task-faceprocessing_desc-SCRAMBLED1_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-06/sub-06_task-faceprocessing_desc-SCRAMBLED2dl_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-06/sub-06_task-faceprocessing_desc-SCRAMBLED2im_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-06/sub-06_task-faceprocessing_desc-UNFAMILIAR1_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-06/sub-06_task-faceprocessing_desc-UNFAMILIAR2dl_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-06/sub-06_task-faceprocessing_desc-UNFAMILIAR2im_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-07/sub-07_task-faceprocessing_desc-FAMOUS1_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-07/sub-07_task-faceprocessing_desc-FAMOUS2dl_effect.nii.gz
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/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-09/sub-09_task-faceprocessing_desc-FAMOUS1_effect.nii.gz
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/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-13/sub-13_task-faceprocessing_desc-FAMOUS1_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-13/sub-13_task-faceprocessing_desc-FAMOUS2dl_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-13/sub-13_task-faceprocessing_desc-FAMOUS2im_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-13/sub-13_task-faceprocessing_desc-SCRAMBLED1_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-13/sub-13_task-faceprocessing_desc-SCRAMBLED2dl_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-13/sub-13_task-faceprocessing_desc-SCRAMBLED2im_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-13/sub-13_task-faceprocessing_desc-UNFAMILIAR1_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-13/sub-13_task-faceprocessing_desc-UNFAMILIAR2dl_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-13/sub-13_task-faceprocessing_desc-UNFAMILIAR2im_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-14/sub-14_task-faceprocessing_desc-FAMOUS1_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-14/sub-14_task-faceprocessing_desc-FAMOUS2dl_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-14/sub-14_task-faceprocessing_desc-FAMOUS2im_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-14/sub-14_task-faceprocessing_desc-SCRAMBLED1_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-14/sub-14_task-faceprocessing_desc-SCRAMBLED2dl_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-14/sub-14_task-faceprocessing_desc-SCRAMBLED2im_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-14/sub-14_task-faceprocessing_desc-UNFAMILIAR1_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-14/sub-14_task-faceprocessing_desc-UNFAMILIAR2dl_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-14/sub-14_task-faceprocessing_desc-UNFAMILIAR2im_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-15/sub-15_task-faceprocessing_desc-FAMOUS1_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-15/sub-15_task-faceprocessing_desc-FAMOUS2dl_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-15/sub-15_task-faceprocessing_desc-FAMOUS2im_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-15/sub-15_task-faceprocessing_desc-SCRAMBLED1_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-15/sub-15_task-faceprocessing_desc-SCRAMBLED2dl_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-15/sub-15_task-faceprocessing_desc-SCRAMBLED2im_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-15/sub-15_task-faceprocessing_desc-UNFAMILIAR1_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-15/sub-15_task-faceprocessing_desc-UNFAMILIAR2dl_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-15/sub-15_task-faceprocessing_desc-UNFAMILIAR2im_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-16/sub-16_task-faceprocessing_desc-FAMOUS1_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-16/sub-16_task-faceprocessing_desc-FAMOUS2dl_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-16/sub-16_task-faceprocessing_desc-FAMOUS2im_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-16/sub-16_task-faceprocessing_desc-SCRAMBLED1_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-16/sub-16_task-faceprocessing_desc-SCRAMBLED2dl_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-16/sub-16_task-faceprocessing_desc-SCRAMBLED2im_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-16/sub-16_task-faceprocessing_desc-UNFAMILIAR1_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-16/sub-16_task-faceprocessing_desc-UNFAMILIAR2dl_effect.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-16/sub-16_task-faceprocessing_desc-UNFAMILIAR2im_effect.nii.gz

3. Displaying subject Effects-Of-Interest z-maps¶

To check how the first-level results look overall, it is helpful to display effects-of-interest for all subjects.

In [6]:
eoi_maps = layout.get(desc='EffectsOfInterest', extension='.nii.gz', return_type='file')
print(*eoi_maps, sep="\n")

/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-01/sub-01_task-faceprocessing_desc-EffectsOfInterest_z.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-02/sub-02_task-faceprocessing_desc-EffectsOfInterest_z.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-03/sub-03_task-faceprocessing_desc-EffectsOfInterest_z.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-04/sub-04_task-faceprocessing_desc-EffectsOfInterest_z.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-05/sub-05_task-faceprocessing_desc-EffectsOfInterest_z.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-06/sub-06_task-faceprocessing_desc-EffectsOfInterest_z.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-07/sub-07_task-faceprocessing_desc-EffectsOfInterest_z.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-08/sub-08_task-faceprocessing_desc-EffectsOfInterest_z.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-09/sub-09_task-faceprocessing_desc-EffectsOfInterest_z.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-10/sub-10_task-faceprocessing_desc-EffectsOfInterest_z.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-11/sub-11_task-faceprocessing_desc-EffectsOfInterest_z.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-12/sub-12_task-faceprocessing_desc-EffectsOfInterest_z.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-13/sub-13_task-faceprocessing_desc-EffectsOfInterest_z.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-14/sub-14_task-faceprocessing_desc-EffectsOfInterest_z.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-15/sub-15_task-faceprocessing_desc-EffectsOfInterest_z.nii.gz
/home/cognestic/COGNESTIC/05_fMRI/FaceProcessing/results/first-level/sub-16/sub-16_task-faceprocessing_desc-EffectsOfInterest_z.nii.gz
In [7]:
subjects = layout.get_subjects()

fig, axes = plt.subplots(nrows=4, ncols=4, figsize=(14, 14))

for i, stat_map in enumerate(eoi_maps):
    plot_glass_brain(stat_map, 
                              title = 'sub-' + subjects[i],
                              axes = axes[int(i / 4), int(i % 4)],
                              plot_abs = False, 
                              display_mode='x')
fig.suptitle('Effects of interest' + ', unthresholded z-maps')
Out[7]:
Text(0.5, 0.98, 'Effects of interest, unthresholded z-maps')
No description has been provided for this image

4. Specify the second-level model¶

At the group-level analysis, we also use a GLM. The outcome variable is the beta/contrast estimate from each subject, and the predictor variables typically include group-level factors such as experimental conditions, subject-specific regressors (in repeated-measures designs), group-specific regressors (in between-subject designs), and subject-specific covariates (e.g., age, gender, or behavioural scores).

4.1. Design matrix¶

In this example, the design matrix we generate will represent a mixed-effects design, incorporating both within-subject (conditions) and between-subject (subjects) factors. Each row in the design matrix corresponds to a specific observation, which in this case is a beta estimate from a given condition and subject, while each column represents a predictor variable.

The number of rows in the design matrix must match the number of first-level result files that will be entered into the second-level model. The order of the rows in the design matrix must match the order of the provided files.

In [8]:
conditions = ['FAMOUS1', 'FAMOUS2dl', 'FAMOUS2im', 'UNFAMILIAR1', 'UNFAMILIAR2dl', 'UNFAMILIAR2im', 'SCRAMBLED1', 'SCRAMBLED2dl', 'SCRAMBLED2im']

# Create an empty DataFrame
df = pd.DataFrame(columns=conditions + subjects)

# Populate the DataFrame with 0s and 1s
for i, condition in enumerate(conditions):
    # Filter files based on condition
    condition_files = [1 if condition in file else 0 for file in effect_files]
    # Add a column for the condition
    df[condition] = condition_files

# Populate the DataFrame with 0s and 1s for subjects
for i, subject in enumerate(subjects):
    # Filter files based on subject
    subject_files = [1 if f"sub-{subject}" in file else 0 for file in effect_files]
    # Add a column for the subject
    df[subject] = subject_files

# Print the resulting DataFrame
design_matrix = df
design_matrix
Out[8]:
FAMOUS1 FAMOUS2dl FAMOUS2im UNFAMILIAR1 UNFAMILIAR2dl UNFAMILIAR2im SCRAMBLED1 SCRAMBLED2dl SCRAMBLED2im 04 ... 07 08 09 10 11 12 13 14 15 16
0 1 0 0 0 0 0 0 0 0 0 ... 0 0 0 0 0 0 0 0 0 0
1 0 1 0 0 0 0 0 0 0 0 ... 0 0 0 0 0 0 0 0 0 0
2 0 0 1 0 0 0 0 0 0 0 ... 0 0 0 0 0 0 0 0 0 0
3 0 0 0 0 0 0 1 0 0 0 ... 0 0 0 0 0 0 0 0 0 0
4 0 0 0 0 0 0 0 1 0 0 ... 0 0 0 0 0 0 0 0 0 0
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
139 0 0 0 0 0 0 0 1 0 0 ... 0 0 0 0 0 0 0 0 0 1
140 0 0 0 0 0 0 0 0 1 0 ... 0 0 0 0 0 0 0 0 0 1
141 0 0 0 1 0 0 0 0 0 0 ... 0 0 0 0 0 0 0 0 0 1
142 0 0 0 0 1 0 0 0 0 0 ... 0 0 0 0 0 0 0 0 0 1
143 0 0 0 0 0 1 0 0 0 0 ... 0 0 0 0 0 0 0 0 0 1

144 rows × 25 columns

In [9]:
ax = plot_design_matrix(design_matrix)
ax.set_title("Second level design matrix", fontsize=12)
ax.set_ylabel("stat maps")
Out[9]:
Text(42.722222222222214, 0.5, 'stat maps')
No description has been provided for this image

4.2. Contrasts¶

For these group-level results, we are only interested in the statistics, not the contrast estimates, so scaling the contrasts is not strictly necessary.

In [10]:
n_columns = design_matrix.shape[1]

contrasts = {
  'Faces_Scrambled': np.pad([1, 1, 1, 1, 1, 1, -2, -2, -2], (0, n_columns - 9), 'constant'),
  'Famous_Unfamiliar': np.pad([1, 1, 1, -1, -1, -1, 0, 0, 0], (0, n_columns - 9), 'constant')
}
In [11]:
for contrast_id, contrast_val in contrasts.items():
    plot_contrast_matrix(contrast_val, design_matrix=design_matrix)
    plt.suptitle(contrast_id)
No description has been provided for this image
No description has been provided for this image

4.3. Model specification and fit¶

In [12]:
# specify
second_level_model = SecondLevelModel() 
# fit
second_level_model = second_level_model.fit(
  effect_files, 
  design_matrix = design_matrix
  )

5. Computing contrasts and plotting result maps¶

In [13]:
# get the z-maps for the contrast
z_map = second_level_model.compute_contrast(
  contrasts['Faces_Scrambled'], 
  output_type='z_score')

5.1. False-positive-rate with cluster-forming threshold¶

In [14]:
thresholded_map_fpr, threshold_fpr = threshold_stats_img(
  z_map, 
  alpha=0.001, 
  height_control='fpr', 
  cluster_threshold=20,
  two_sided=True)
In [15]:
print('Uncorrected p<.001 threshold: %.3f' % threshold_fpr)

plot_stat_map(
    thresholded_map_fpr,
    bg_img = mni152_template, 
    threshold=threshold_fpr,   
    display_mode = 'ortho',
    black_bg = True,    
    title = 'Faces > Scrambled  (p<.001, uncorrected, k=20)'
    )

fig = plt.gcf()
fig.set_size_inches(10,3)
plt.show()

Uncorrected p<.001 threshold: 3.291
No description has been provided for this image
In [16]:
# Interactive plotting
plot = view_img(
  thresholded_map_fpr, 
  bg_img=mni152_template, 
  threshold=threshold_fpr, 
  colorbar=True, 
  title='Faces > Scrambled  (p < .001, uncorrected)'
  )

plot.open_in_browser()

/cognestic/miniconda3/envs/mri/lib/python3.11/site-packages/numpy/core/fromnumeric.py:771: UserWarning: Warning: 'partition' will ignore the 'mask' of the MaskedArray.
  a.partition(kth, axis=axis, kind=kind, order=order)

5.2. FWE correction using Bonferroni correction¶

In [17]:
thresholded_map_bonf, threshold_bonf = threshold_stats_img(
  z_map, 
  alpha=0.05, 
  height_control='bonferroni', 
  cluster_threshold=20,
  two_sided=False)

print('Bonferroni p<.05 threshold: %.3f' % threshold_bonf)

plot_stat_map(
    thresholded_map_bonf, 
    bg_img = mni152_template,
    threshold=threshold_bonf,   
    display_mode = 'ortho',
    black_bg = True,
    cmap = 'hot',    
    title = 'Faces > Scrambled  (Bonf. p<.05, k=20)'
    )

fig = plt.gcf()
fig.set_size_inches(10,3)
plt.show()

Bonferroni p<.05 threshold: 5.072
No description has been provided for this image

5.3. FWE correction using non-parametric permutation testing¶

Nilearn's FWE correction using the Bonferroni approach (height_control='bonferroni') is applied to the number of voxels. However, this method is not well-suited for fMRI data because neuroimaging data typically exhibit spatially correlated data points, which violate the Bonferroni assumption of independent tests.

As an alternative, neuroscientists have developed Random Field Theory (RFT), which accounts for spatial correlations by applying multiple comparison corrections that consider the smoothness of the data. Specifically, the correction is applied to the number of 'resels' (RESolution ELements), rather than the raw number of voxels. However, it's important to note that this RFT-based approach is not implemented in Nilearn. At the group level, Nilearn provides an option for non-parametric inference with permutation testing, which is a more appropriate approach for fMRI data when accounting for the spatial correlation of voxels.

(More on non-parametric permutation testing, have a look at Rik's Stats notebook.)

In [18]:
out_dict = non_parametric_inference(
    effect_files,
    design_matrix = design_matrix,
    second_level_contrast = contrasts['Faces_Scrambled'],
    n_perm = 100, # ideally at least 10000
    two_sided_test = False,
    n_jobs = -1, # Use all available cores
    threshold = 0.001 # cluster level threshold; enables cluster-level inference
)

# Print the keys of the output dictionary
print(out_dict.keys())

/cognestic/miniconda3/envs/mri/lib/python3.11/site-packages/nilearn/mass_univariate/permuted_least_squares.py:986: UserWarning: Data array used to create a new image contains 64-bit ints. This is likely due to creating the array with numpy and passing `int` as the `dtype`. Many tools such as FSL and SPM cannot deal with int64 in Nifti images, so for compatibility the data has been converted to int32.
  image.new_img_like(masker.mask_img_, metric_map),
/cognestic/miniconda3/envs/mri/lib/python3.11/site-packages/nilearn/masking.py:980: UserWarning: Data array used to create a new image contains 64-bit ints. This is likely due to creating the array with numpy and passing `int` as the `dtype`. Many tools such as FSL and SPM cannot deal with int64 in Nifti images, so for compatibility the data has been converted to int32.
  return new_img_like(mask_img, unmasked, affine)

dict_keys(['t', 'logp_max_t', 'size', 'logp_max_size', 'mass', 'logp_max_mass'])

The output is multiple images (maps), organised in a dictionary.

  • Voxel-level inference
    • t: t-statistics
    • logp_max_t: Negative log10 family-wise error rate-corrected p-values corrected based on the distribution of maximum t-statistics from permutations.
  • Cluster-level inference
    • size: Cluster size values associated with the significance test
    • logp_max_size: Negative log10 family-wise error rate-corrected p-values corrected based on the distribution of maximum cluster sizes from permutations.
    • mass: Cluster mass values associated with the significance test
    • logp_max_mass: Negative log10 family-wise error rate-corrected p-values corrected based on the distribution of maximum cluster masses from permutations.

We will focus only on the voxel-level inference.

To report the FWE-corrected maps, we could display the logp_max_t; however, these values can be difficult to interpret if you're not familiar with them. It might be better to plot and report a t-map, masked to exclude the voxels that did not survive the FWE correction.

Let's create a new image displaying t-values for the voxels with a p-value < 0.05.

In [19]:
alpha = 0.05
masked = out_dict['logp_max_t'].get_fdata() > -np.log10(alpha)
masked_t_map = out_dict['t'].get_fdata() * masked

# save the masked t-map as a nifti image
masked_t_map_img = nib.Nifti1Image(masked_t_map, out_dict['t'].affine)
In [20]:
# Get the smallest t-value that is above the threshold (for the colorbar; the maps themselves are thresholded already)
threshold_fwe = masked_t_map[masked_t_map > 0].min()
print('FWE (perm.) p<.05 threshold: %.3f' % threshold_fwe)

plot_stat_map(
    masked_t_map_img, 
    threshold = threshold_fwe,       
    display_mode = 'ortho',
    black_bg = True,
    bg_img = mni152_template,
    cmap = 'hot',
    title = f"Faces > Scrambled (FWE p <.{alpha})")

fig = plt.gcf()
fig.set_size_inches(10,3)
plt.show()

FWE (perm.) p<.05 threshold: 5.052
No description has been provided for this image

In this example, we observe that the non-parametric FWE correction is slightly less conservative than the Bonferroni correction.

6. Summary results¶

6.1. Using atlasreader package¶

We can use 'atlasreader' package to get summary results (peak table, cluster table, .png images of each cluster).

In [21]:
# generate and save atlasreader output
outdir = op.join(fmri_results_dir, 'group-level', 'permutation', 'FacesScrambled')

create_output(
    masked_t_map_img, 
    cluster_extent = 20, 
    voxel_thresh = threshold_fwe,
    direction = 'pos',
    outdir = outdir
)
In [22]:
# display the peak table
peaks = glob.glob(op.join(outdir, '*_peaks.csv'))
display(pd.read_csv(peaks[0]))
cluster_id peak_x peak_y peak_z peak_value volume_mm aal desikan_killiany harvard_oxford
0 1.0 35.5 -88.5 -12.5 11.110699 4640.0 Occipital_Inf_R ctx-rh-lateraloccipital 47.0% Right_Lateral_Occipital_Cortex_inferior_...
1 2.0 -42.5 -56.5 -18.5 9.219398 3752.0 Fusiform_L ctx-lh-fusiform 51.0% Left_Temporal_Occipital_Fusiform_Cortex;...
2 3.0 41.5 -48.5 -18.5 8.760171 2640.0 Fusiform_R Right-Cerebral-White-Matter 54.0% Right_Temporal_Occipital_Fusiform_Cortex...
3 4.0 -2.5 55.5 -12.5 6.732617 1184.0 Frontal_Med_Orb_L Unknown 42.0% Left_Frontal_Medial_Cortex; 42.0% Left_F...
4 5.0 45.5 -60.5 13.5 5.959128 456.0 Temporal_Mid_R Right-Cerebral-White-Matter 34.0% Right_Lateral_Occipital_Cortex_inferior_...
5 6.0 -20.5 -8.5 -14.5 7.706945 456.0 Hippocampus_L Left-Amygdala 94.0% Left_Amygdala
6 7.0 21.5 -6.5 -16.5 7.084664 352.0 Hippocampus_R Right-Amygdala 90.0% Right_Amygdala; 5.0% Right_Hippocampus
In [23]:
# display the cluster table
clusters = glob.glob(op.join(outdir, '*_clusters.csv'))
display(pd.read_csv(clusters[0]))
cluster_id peak_x peak_y peak_z cluster_mean volume_mm aal desikan_killiany harvard_oxford
0 1.0 35.5 -88.5 -12.5 7.013358 4640.0 87.07% Occipital_Inf_R; 5.00% Fusiform_R 46.38% Right-Cerebral-White-Matter; 43.45% ctx... 64.31% Right_Lateral_Occipital_Cortex_inferior...
1 2.0 -42.5 -56.5 -18.5 6.271471 3752.0 58.21% Fusiform_L; 22.81% Occipital_Inf_L; 7.8... 33.69% Left-Cerebral-White-Matter; 24.09% ctx-... 41.15% Left_Temporal_Occipital_Fusiform_Cortex...
2 3.0 41.5 -48.5 -18.5 6.360162 2640.0 76.67% Fusiform_R; 15.76% Temporal_Inf_R 41.82% ctx-rh-fusiform; 37.27% Right-Cerebral-... 92.12% Right_Temporal_Occipital_Fusiform_Corte...
3 4.0 -2.5 55.5 -12.5 5.525319 1184.0 42.57% Frontal_Med_Orb_L; 27.03% Rectus_L; 15.... 77.70% Unknown; 12.84% ctx-lh-medialorbitofron... 43.92% Left_Frontal_Medial_Cortex; 40.54% Righ...
4 5.0 45.5 -60.5 13.5 5.306312 456.0 100.00% Temporal_Mid_R 33.33% Right-Cerebral-White-Matter; 26.32% ctx... 42.11% Right_Lateral_Occipital_Cortex_inferior...
5 6.0 -20.5 -8.5 -14.5 5.937937 456.0 47.37% Hippocampus_L; 35.09% Amygdala_L; 17.54... 59.65% Left-Amygdala; 14.04% Left-VentralDC; 1... 92.98% Left_Amygdala; 7.02% Left_Hippocampus
6 7.0 21.5 -6.5 -16.5 5.705124 352.0 68.18% Hippocampus_R; 31.82% Amygdala_R 63.64% Right-Amygdala; 20.45% Right-Hippocampu... 79.55% Right_Amygdala; 20.45% Right_Hippocampus

Some more plotting options

In [24]:
# get the top 5 peaks' x values
x = pd.read_csv(peaks[0])['peak_x'][:5]
# sort the x values
x = x.sort_values()

# plot these peaks
plot_stat_map(
    masked_t_map_img, 
    threshold = threshold_fwe,       
    display_mode = 'x',
    cut_coords = x,
    black_bg = True,
    bg_img = mni152_template,
    cmap = 'hot',
    title = f"Faces > Scrambled (FWE p <.{alpha})")

fig = plt.gcf()
fig.set_size_inches(15,3)
No description has been provided for this image

We can also look at a 3D brain using plotly.

In [25]:
view = view_img_on_surf(masked_t_map_img, 
    threshold = threshold_fwe)
#view.open_in_browser()
view.resize(1600, 800)
view
Out[25]:

Or use, for example, FSLeyes to plot and explore the result maps.

6.2. Nilearn's report¶

Nilearn has a built-in report generator that can create reports for all defined contrasts. However, a limitation is that it cannot generate reports for results obtained using non-parametric inference.

In [26]:
second_level_report = second_level_model.generate_report(
  contrasts, 
  title="Results of the second-level analysis", 
  bg_img=mni152_template, 
  alpha=0.001, 
  cluster_threshold=20, 
  height_control='fpr', 
  min_distance=8.0, 
  plot_type='slice', 
  display_mode='x', 
  report_dims=(1600, 800))

second_level_report.open_in_browser()

EXCERCISE¶

Perform a one-sample t-test on the first-level results of Faces > Scrambled contrast. How do the results compare to our mixed-effect model approach above?

In [ ]: